You are of course correct. But then, if you do that, the first political issue your church might be interested in promoting would be a flat tax or the Fair Tax - neither of which would have the charitable deduction for yourself or anyone else.
If it were my church I'd hope the first political issue would be Abortion...as well as the second and perhaps the third. The legal holocaust we have permitted in this nation is an abomination.
After that, I would (were I the decision maker on it) chose to address poverty and adoptions. If the church can show how successfully it can do what the government does so poorly perhaps we could get rid of the onerous and grossely inefficient social welfare projects the democrats have loaded into our government by replacing them through church programs. Get rid of that junk and you've gotten rid of over half the government budget.
If the Church isn't tied to the government through tax exempt conditions and government financing of Church programs then the Church will be free to promote the gospel while they pursue feeding the poor, the homeless and the orphans.